By working in a Metric-Affine approach (i.e. considering the metric and the connection as independent variables) we have considered a generalized version of the theory proposed in [1]}. In particular, we derived the full set of field equations of the class of theories whose gravitational part of the Lagrangian is given by \(F(R,T,Q,{\cal T}, {\cal D})\) , where \(T\) , \(Q\)  are the torsion and non-metricity scalars, \({\cal T}\)  is the trace of the energy-momentum tensor and \({\cal D}\)  is the divergence of the dilation current (one of the hypermomentum sources). The family of theories contained in our Lagrangian is fairly large since all, metric and Palatini \(f(R)\)  theories, teleparallel \(f(T)\) , symmetric teleparallel \(f(Q)\)  or even generalized teleparallel \(f(G)\)  and generalizations of them such as \(f(R, {\cal T})\) , \(f(T,{\cal T} )\) , \(f(Q,{\cal T} )\)  can be seen as special cases of our theory.
